Graph y=sin(5x)

Problem

y=sin(5*x)

Solution

1. Identify the parent function and its properties. The function is of the form y=A*sin(B*x) where the parent function is y=sin(x)

2. Determine the amplitude, which is the absolute value of the coefficient A Here, A=1 so the amplitude is 1 This means the graph oscillates between y=1 and y=−1

3. Calculate the period using the formula P=(2*π)/|B| In this function, B=5

P=(2*π)/5

4. Find the key points by dividing the period into four equal intervals. The increment is P/4=(2*π)/20=π/10

5. Evaluate the function at the key xvalues starting from x=0

• At x=0 y=sin(0)=0

• At x=π/10 y=sin(π/2)=1

• At x=π/5 y=sin(π)=0

• At x=(3*π)/10 y=sin((3*π)/2)=−1

• At x=(2*π)/5 y=sin(2*π)=0

6. Sketch the curve by plotting these points and connecting them with a smooth wave. The graph is a horizontal compression of y=sin(x) by a factor of 5

Final Answer

y=sin(5*x)

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